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%I #18 Sep 27 2018 11:10:24
%S 1,1,1,-1,1,0,1,1,1,-1,0,-1,1,-1,1,0,1,1,-1,1,0,1,-1,1,-1,1,-2,1,-1,1,
%T -1,1,0,1,1,1,-1,0,-1,1,-1,1,-1,2,-2,2,-1,2,-2,1,-2,2,-2,1,-1,1,-1,1,
%U 0,1,1,-1,1,0,1,-1,1,-1,1,-2,2,-2,2,-3,2,-2,3,-3,3,-2,3,-3,3,-2,2,-3,2,-2,2,-2,1,-1,1,-1,1,0,1,1
%N Irregular triangle array of coefficients in ascending order of modified polynomials that arise in the study of Erdős-Ko-Rado sets of generators of the hyperbolic quadrics Q+(4n + 1, q).
%C The n-th polynomial, as described in the link, is divisible by x^(n*(n-1)).
%C So they are here divided by this factor, thus removing the n*(n-1) leading zeros from the n-th row.
%C The initial degree of the n-th polynomial was n*(2*n-1) (A000384), so, finally the length of the n-th row is n^2 + 1 (A002522).
%C It appears this sequence is identical to A178666 up to the signs.
%H Maarten De Boeck, <a href="http://arxiv.org/abs/1601.03543">The second largest Erdős-Ko-Rado sets of generators of the hyperbolic quadrics Q+(4n+1,q)</a>, arXiv:1601.03543 [math.CO], 2016. See page 5.
%F Pol(n) = (q^(n^2-n)*Prod_{k=1..n} (q^(2*k-1)-1) + 2*Sum_{i=0..n-1} gauss_binomial(2*n,2*i,q)*q^(i^2-i)*Prod_{k=1..i}(q^(2*k-1)-1))/q^(n^2-n), where gauss_binomial(j,k,q) = Prod_{i=1..k} (q^(j+1-i)-1)/(q^i-1)).
%e The rows with leading zeros are:
%e [1],
%e [1, 1],
%e [0, 0, -1, 1, 0, 1, 1],
%e [0, 0, 0, 0, 0, 0, 1, -1, 0, -1, 1, -1, 1, 0, 1, 1].
%e The leading zeros are dropped, so the triangle starts:
%e [1],
%e [1, 1],
%e [-1, 1, 0, 1, 1],
%e [1, -1, 0, -1, 1, -1, 1, 0, 1, 1],
%e [-1, 1, 0, 1, -1, 1, -1, 1, -2, 1, -1, 1, -1, 1, 0, 1, 1].
%t gbinom[n_, k_, q_] := Product[(q^(n + 1 - i) - 1)/(q^i - 1), {i, 1, k}];
%t g[n_] := (q^(n^2 - n) Product[q^(2k-1)-1, {k, 1, n}] + 2 Sum[gbinom[2n, 2i, q] q^(i^2-i) Product[q^(2k-1)-1, {k, 1, i}], {i, 0, n-1}])/q^(n^2-n);
%t row[n_] := CoefficientList[g[n], q];
%t Table[row[n], {n, 0, 6}] // Flatten (* _Jean-François Alcover_, Sep 27 2018, from PARI *)
%o (PARI) gbinom(n,k,q) = prod(i=1,k, (q^(n+1-i)-1)/(q^i-1));
%o g(n) = (q^(n^2-n)*prod(k=1, n, q^(2*k-1)-1) + 2*sum(i=0,n-1,gbinom(2*n,2*i,q)*q^(i^2-i)*prod(k=1,i,q^(2*k-1)-1)))/q^(n^2-n);
%o row(n) = Vecrev(g(n));
%Y Cf. A000384, A002378, A002522, A178666.
%K sign,tabf
%O 0,27
%A _Michel Marcus_, Jan 18 2016
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